Many biological tissues and organisms are in a state of residual stress, which should be considered rather than ignored as in many previous studies. In this work, we establish a theoretical model to study the growth and patterns of a residually stressed core–shell soft sphere. The effect of the initial residual stress is considered by employing a modified multiplicative decomposition growth model. Numerical solution of the marginal instability relies on gaining a critical differential growth ratio which depends on the initial residual stress, geometry, and material elasticity. Results show that the initial residual stress can not only well regulate the growth procedure but also affect the critical pattern of the growing instability. Compared with the way of changing material elasticity or geometrical size, it is more effective in practice. This work may help understand the morphological transition of residually stressed soft matters, and provide insights into the growth self-assembly and biomedical engineering.

许多生物组织和生物体处于残余应力状态，在许多先前的研究中应考虑而不是忽略这些残余应力。在这项工作中，我们建立了一个理论模型来研究残余应力核壳软球的生长和模式。通过采用改进的乘法分解增长模型来考虑初始残余应力的影响。边际不稳定性的数值解依赖于获得临界的微分增长率，该增长率取决于初始残余应力，几何形状和材料弹性。结果表明，初始残余应力不仅可以很好地调节生长过程，而且可以影响生长不稳定的临界模式。与改变材料弹性或几何尺寸的方式相比，在实践中更有效。